Solve 1-x-2/6leq2x-1/3

$$1 - \frac { x - 2 } { 6 } \leq \frac { 2 x - 1 } { 3 }$$

Solve for x

$$x\geq 2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 6,3. Since 6 is positive, the inequality direction remains the same.

$$6-\left(x-2\right)\leq 2\left(2x-1\right)$$

To find the opposite of x-2, find the opposite of each term.

$$6-x-\left(-2\right)\leq 2\left(2x-1\right)$$

The opposite of -2 is 2.

$$6-x+2\leq 2\left(2x-1\right)$$

Add 6 and 2 to get 8.

$$8-x\leq 2\left(2x-1\right)$$

Use the distributive property to multiply 2 by 2x-1.

$$8-x\leq 4x-2$$

Subtract 4x from both sides.

$$8-x-4x\leq -2$$

Combine -x and -4x to get -5x.

$$8-5x\leq -2$$

Subtract 8 from both sides.

$$-5x\leq -2-8$$

Subtract 8 from -2 to get -10.

$$-5x\leq -10$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\geq \frac{-10}{-5}$$

Divide -10 by -5 to get 2.

$$x\geq 2$$